Atomic Energy Levels and Line Spectra

Take the energy of an electron separated from the atom at rest as zero. Bound levels have negative values because energy must be supplied to remove the electron. A ground state is the lowest available level; excited states are higher but can still be negative.

An electron can absorb an appropriate amount of energy and move to a higher allowed level. A transition down emits a photon whose energy equals the positive difference between the two levels. Use the level difference, not the magnitude of either level alone.

A hot dense source produces an approximately continuous spectrum. A low-pressure excited gas produces emission lines at allowed photon energies. A continuous spectrum passing through a cooler gas shows absorption lines where atoms absorb photons that match transitions from populated lower levels.

Each element has a characteristic set of energy levels and hence a distinctive pattern of lines. Comparing stellar and laboratory patterns identifies elements, allowing for Doppler shifts that move the overall pattern. A weak line does not necessarily mean an element is absent: excitation and ionisation also matter.

A transmission grating sends a given wavelength into maxima satisfying d sinθ=nλ. Convert line density to spacing in metres before calculation, measure angles relative to the central maximum and identify the order n.

Measuring symmetric orders on both sides can reduce alignment error. Distinct wavelengths produce distinct angular positions, making spectra useful for identifying line patterns. The detailed structure of an optical spectrometer is outside the required OCR treatment, but the grating relation and measurement geometry are required.

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.